He played Shane Parrish in the popular Australian soap from 1992 until 1996.
On-screen, Brummer’s character was married to Angel, played by Melissa George.
He was also Troy Miller in rival soap Neighbours and had roles in shows Underbelly and Winners And Losers.
Brummer’s former Home And Away co-star Emily Symons, who played Marilyn Chambers, posted a tribute on Instagram.
She wrote: “I can’t believe this absolutely tragic news. Dieter was such a lovely, kind, genuine person. I always enjoyed working with him.
“I will never forget his beautiful smile, he was a much loved member of our Home and Away family. Thinking of his loved ones at this difficult time.”
Lynne McGranger, who plays Irene Roberts on the soap, tweeted: “So very sad. Please reach out. Ask if people are doing ok. And tell someone if YOU’RE not ok!”
A statement on the official Instagram page of the programme said: “Home and Away and @channel7 are deeply saddened to hear of Dieter Brummer’s passing.
“Dieter was a much-loved Home and Away cast member and celebrated by Australian and international audiences for his award-winning portrayal of Shane Parrish.
“We send our sincere condolences to Dieter’s family and friends during this very difficult time.”
Home And Away star Georgie Parker, known as Roo Stewart in the soap, wrote: “Such sad news, such a lovely man and a good actor too.
“Much love to his family and loved ones at this terribly difficult time.”
Fellow Australian soap Neighbours also shared a tribute to Brummer, with a post on Instagram reading: “Vale Dieter Brummer, joined the Neighbours alumni in 2012 as Capt Troy Miller.
“Our thoughts are with his family and friends.”
Scott McGregor, who played Detective Mark Brennan in Neighbours, said: “Rest In Peace old mate. Such a special human. Ill never forget our motorbike weekend.”
Derry Girls creator and writer Lisa McGee said: “Incredibly sad news about Dieter Brummer. I have such fond memories of watching him play Shane in #HomeandAway”
A statement from the New South Wales Police said: “About 1.30pm (Saturday July 24 2021), officers from The Hills Police Area Command responded to reports of a concern for welfare at a home on Glenhaven Road, Glenhaven.
“The body of a man was located inside the home.
“His death is not believed to be suspicious.
“A report will be prepared for the information of the coroner.”